At 3rd level Monks gain +10ft fast movement. At 4th level a Shoei gains Monastic mount replacing fast movement. Does this mean a Shoei's base speed increases to 40ft at 3rd and stays at 40ft or does their speed drop at 4th level?
No, the fast movement class feature is replaced for the sohei - they never get the first +10' bonus. That they don't get anything until 4th level may seem slightly unfair if you're looking at those two class features alone, but it's a strong archetype and there's really no grounds for complaint.